Foundations of Mathematical Economics

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Overview

This book provides a comprehensive introduction to the mathematical foundations of economics, from basic set theory to fixed point theorems and constrained optimization. Rather than simply offer a collection of problem-solving techniques, the book emphasizes the unifying mathematical principles that underlie economics. Features include an extended presentation of separation theorems and their applications, an account of constraint qualification in constrained optimization, and an introduction to monotone comparative statics. These topics are developed by way of more than 800 exercises. The book is designed to be used as a graduate text, a resource for self-study, and a reference for the professional economist.
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What People Are Saying

From the Publisher
"This book extends the study of evolutionary dynamics to extensive form games,shifting seamlessly between biological foundations, mathematical tools and economic applications. It will be an essential resource for anyone interested in the evolutionary foundations of behavior."—Larry Samuelson, Department of Economics, University of Wisconsin—Madison

"This book should be an obvious choice for graduate courses or as a research reference. The integration of exercises and economic applications is especially helpful."—LarrySamuelson, Department of Economics, University of Wisconsin—Madison

"Michael Carter's lucid exposition of a wide range of mathematical tools is essential reading for graduate students of economics. His marvelous collection of up-to-date examples perfectly complements his exposition of the theory."—Martin J. Osborne, Department of Economics,University of Toronto

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Product Details

  • ISBN-13: 9780262032896
  • Publisher: MIT Press
  • Publication date: 10/1/2001
  • Pages: 365
  • Product dimensions: 8.00 (w) x 9.00 (h) x 1.25 (d)

Meet the Author

Michael Carter is Visiting Professor at the University of Hohenheim, Germany.

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Table of Contents

Introduction
A Note to the Reader
1 Sets and Spaces 1
1.1 Sets 1
1.2 Ordered Sets 9
1.3 Metric Spaces 45
1.4 Linear Spaces 66
1.5 Normed Linear Spaces 114
1.6 Preference Relations 130
2 Functions 145
2.1 Functions as Mappings 145
2.2 Monotone Functions 186
2.3 Continuous Functions 210
2.4 Fixed Point Theorems 232
3 Linear Functions 263
3.1 Properties of Linear Functions 269
3.2 Affine Functions 276
3.3 Linear Functionals 277
3.4 Bilinear Functions 287
3.5 Linear Operators 295
3.6 Systems of Linear Equations and Inequalities 306
3.7 Convex Functions 323
3.8 Homogeneous Functions 351
3.9 Separation Theorems 358
4 Smooth Functions 417
4.1 Linear Approximation and the Derivative 417
4.2 Partial Derivatives and the Jacobian 429
4.3 Properties of Differentiable Functions 441
4.4 Polynomial Approximation 457
4.5 Systems of Nonlinear Equations 467
4.6 Convex and Homogeneous Functions 483
5 Optimization 497
5.1 Introduction 497
5.2 Unconstrained Optimization 503
5.3 Equality Constraints 516
5.4 Inequality Constraints 549
6 Comparative Statics 601
6.1 The Envelope Theorem 603
6.2 Optimization Models 609
6.3 Equilibrium Models 622
References 635
Index of Symbols 641
General Index 643
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